Bond Duration and Convexity Concepts and Exercise (CFA Video)

Question:

ABC bond is currently trading at $910. It has duration = 7 and convexity = 40. Assume the interest rate falls by 60 basis points. What will be the new price?

Answer:

This question tests if you can:

1. Understand the concepts of duration and convexity
2. Properly use the equation
3. Properly apply the signs

Bond price is a function of interest rate and usually inversely related to the interest rate. The relative change of bond price (Delta_P/P) is related to the change of interest rate (Delta_i) by the following equation:

(Delta_P)/P = – D*Delta_i + C* Delta_i²

Where D is the duration and C is the convexity describing the first and second order effects of the Delta_i on the (Delta_P/P).

The equation is simple but one has to remember that:

1)      This equation is about the relative change of price not the absolute one

2)      It has a negative sign before D

3)      It has a positive sign before C

Therefore, 60 basis points reduction is -0.6%. Make sure to substitute -0.006 instead of just -0.6.

Therefore,

(Delta_P)/P = – 7 * (-0.006) + 40 * (-0.006)² = 0.04344

And,

New P = P + Delta_P = P(1+0.04344) = 949.5